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If f = alpha y hat(i)+2alpha x hat(j) ca...

If `f = alpha y hat(i)+2alpha x hat(j)` calculate the work done if a particle moves along path as shown in (given `alpha=1`).

Text Solution

Verified by Experts

The correct Answer is:
`-0.75`
`dw = vec(F).dvec(r )`
`dw = alpha y dx + 2alpha x dy`
`A rarr B y = 1, dy = 0 W_(ArarrB)= int alpha ydx = alpha. 1 int_(0)^(1)dx = alpha`
`B rarr C x = 1, dx = 0 W_(B rarr C) = 2alpha.1 int_(1)^(0.5) dy = -2alpha (0.5)= -alpha`
`C rarr D y = 0.5 dy = 0 W_(C rarr D) = int_(1)^(0.5)alpha y dx`
`= alpha. (1)/(2)int_(1)^(0.5)dx= -(alpha)/(4)`
`D rarr E x=0.5 dx = 0 W_(D rarr E) = 2alpha int xdy = 2alpha. (1)/(2) int_(0.5)^(0)dy = -(alpha)/(2)`
`:. w = alpha - alpha -(alpha)/(4)-(alpha)/(2)=-(3alpha)/(4)`
Given `alpha =1`
`W = -(3)//(4)`
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